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Project funded by the European Commission under Grant Agreement n°696656
Graphene Core 1 Graphene-Based Disruptive Technologies
Horizon 2020 RIA
WP14 Nanocomposites Deliverable 14.3 “Report on electrical percolation of
2D materials in 3D composites”
Main Author(s):
Dimitrios Papageorgiou, UNIMAN
Alex Marsden, UNIMAN
Christina Valles, UNIMAN
Robert Young, UNIMAN
Ian Kinloch, UNIMAN
Julio Gomez, AVA
Jonathon Coleman, TCD
Andrea Liscio, CNR
Vincenzo Palermo, CNR
Due date of deliverable: M12
Actual submission date: M12
Dissemination level: Public
Graphene Core 1 D14.3 31 March 2017 2/ 22
List of Contributors
Partner Acronym Partner Name Name of the contact
2 CNR Consiglio Nazionale delle Ricerche Vincenzo Palermo
6 UMAN University of Manchester Ian Kinloch
31 AVA AVANZARE Julio Gomez
46 TCD Trinity College Dublin Jonathon Coleman
Graphene Core 1 D14.3 31 March 2017 3/ 22
TABLE OF CONTENTS
List of Contributors ................................................................................................... 2
Summary .................................................................................................................... 4
1. Intrinsic Electrical Conductivity of Graphene Derivatives ........................... 4
2. Fundamental Aspects of Electrical Conductivity .......................................... 61.1. Percolation Theory .................................................................................................... 61.2. Conduction Mechanisms in Single Sheets ............................................................. 71.3. Conduction Mechanisms in 2D multilayered systems .......................................... 7
3. Influence of Graphene Morphology on Composite Properties .................... 81.4. Model graphene composites .................................................................................... 81.5. Graphene nanoplatelets ........................................................................................... 91.6. Thermally Reduced Graphene Oxide (TrGO) Composites .................................. 111.7. Chemically Reduced Graphene Oxide Composites ............................................. 12
4. Comparison with other carbonaceous particles ......................................... 13
5. Effect of strain on percolated networks ....................................................... 13
Conclusions ............................................................................................................. 14
References ............................................................................................................... 15
Graphene Core 1 D14.3 31 March 2017 4/ 22
Summary Composites are one of the most promising applications for graphene, where graphene can
be used to the give increase performance of the host matrix, including mechanical stiffness
and strength, thermal stability, thermal conductivity, barrier properties, and sensing abilities.
Graphene could be particularly useful when added to insulating materials such as polymers:
polymers are extremely versatile, but their insulating nature (apart from a few exceptions1)
limits their application in a range applications for conductive adhesives, electrostatic painted
components, lightning strike protection, earthed products, EM shielding and materials for
anti-static applications. However, adding materials to a matrix can also alter other properties,
and these can be potentially degrading. Thus, careful balance is required between addition
and the resulting performance. To further the development of conducting composites, a
detailed understanding of the way charge percolates through the composite is essential.
In this report, we review the progress in the understanding of charge percolation in
composites and how this has led to an improvement in conducting, graphene-based
composites. The conductive properties of intrinsic graphene are discussed initially,
highlighting the importance of production route and morphology on the resulting physical and
electrical properties. The fundamentals of electrical percolation are presented, with a focus
on percolation and hopping transport. We then review recent results on the electrical
properties of graphene-based composites, with Table 1 (Appendix) summarising the reported
composite conductivities as a function of production method and graphene type highlighted.
Finally, the effect of strain on the conducting composites is discussed.
1. Intrinsic Electrical Conductivity of Graphene Derivatives The extremely high conductivity of graphene is one of its most attractive properties. This
conductivity arises from the combination of the high charge carrier mobility and the high
charge carrier concentration present in doped graphene. The conductivity, however, is very
sensitive to the material’s environment and quality. For example, the interaction of graphene
with its substrate has an significant influence with the highest conductivity (6×105 S/m) being
measured on suspended sheets 1. Furthermore, these measurements were performed on
high quality, mechanically exfoliated graphene; a method that is not suitable for industrial
scale production. There are, of course more technologically viable production routes, but
each of these comes with some deterioration of graphene’s properties.
Chemical vapour deposition (CVD) can produce large areas of monolayer 2 or multilayer
graphene depending on the growth conditions used. The measured conductivities of CVD
graphene are less than that of mechanically exfoliated graphene mainly due to its
Graphene Core 1 D14.3 31 March 2017 5/ 22
polycrystalline nature leading to grain boundaries that scatter charges 3. However, recent
developments have opened up the possibility of growing CVD crystal graphene 4,5.
A more relevant choice for composites is graphene nanoplatelets (GNPs) which are typically
much cheaper than other GRMs and available at the tonne scale. Production methods vary,
but most exfoliate bulk graphite using thermal expansion and/or mechanical agitation. The
dimensions, primarily the thickness, of GNPs dictate their intrinsic conductivity, with thinner
GNPs having the highest values; GNPs with a thickness of 50, 5 and 3 nm have conductivity
of 7×104 S/m, 1×105 S/m and 1.5×105 S/m respectively 6. The reason for this thickness effect
is thought to be in the poor between plane conductivity of graphite. Thus, producing thin
flakes remains a priority for conductive composites. The lateral dimensions of GNPs also
play a role, however, less towards their intrinsic conductivity but more to achieving the
percolation threshold at lower contents and minimising flake-to-flake resistance.
Graphite oxide (GO) is produced by the Hummers method 7 or modern modified versions that
are less polluting/safer 8. These routes are scalable and result in monolayer GO 9. The
covalent functionalization of GO has a dramatic impact on its conductivity with reported
values generally around 2×10-2 S/m 9, significantly lower than those of graphene, and this
renders GO unusable for most electrical applications. The covalent functionalization of GO,
however, is reversible to a certain extent, and some electrical conductivity can be recovered.
Reduction routes (yielding reduced graphene oxide, rGO) generally follow thermal routes
(thermally reduced GO, TrGO), or chemical routes (chemically reduced, CrGO).
Chemical reduction involves the exposure of GO to aggressive reduction agents, most
commonly hydrazine. A bulk powder of rGO formed after exposure of hydrazine recovered a
conductivity of 200 S/m 9. Similar values were also obtained from individual monolayers (50-
200 S/m) 10. Another chemical treatment was with immersion in FeI2 at 95°C, which
recovered a conductivity to 6×104 S/m 11.
Thermal treatments have also been applied successfully, and generally perform better at
recovering conductivity. rGO thin films displayed conductivities of ≈5×104 S/m after being
heated to 1100°C whilst still maintaining 80% transmittance 12. As a comparison, the same
study found a hydrazine treatment with annealing at 400°C gave ≈5000 S/m. More recently,
thin films of rGO have reached 9×104 S/m, after annealing at 1000°C in a Ar/H2
atmosphere13. Finally, heating to very high temperatures >2000°C using arc discharge can
recover conductivities of 2x105 S/m 14. Despite success, these reduction methods have not
been able to recover the pristine conductivity of graphene (~9×104 S/m from an rGO thin film
after Ar/H2 heating to 1000°C 13 c.f. free standing graphene 6×105 S/m 1). This difference is
thought to be because only isolated conductive regions of graphene are recovered, and
electrons are required to hop between these regions, reducing the conductivity 10. Further,
even full removal of oxygen containing groups does not recover graphene’s properties, as
Graphene Core 1 D14.3 31 March 2017 6/ 22
defects in the graphene lattice remain, reducing the conductivity. For this reason, covalently
functionalized graphene may not be a suitable material for high-end electrical applications,
and flakes that remain unmodified are likely to be more advantageous 15.
Coleman et al. exfoliated graphene in a liquid using surfactants, rather than functionalization
to stabilise the sheets16. Flakes typically 1-10 layers thick and with lateral size of 500-1000
nm were produced17,18. This route is yields large volumes of graphene that is solution
processeable and high quality with very little defects, and thus should be an excellent
conductor. Indeed, inkjet-printed thin films had conductivities of 3000 S/m 19.
2. Fundamental Aspects of Electrical Conductivity
1.1. Percolation Theory
The versatility and multifunctionality of
polymers make them attractive for several
applications, however the majority of
polymers are classified as insulating and
cannot be used in applications where
electrical conductivity is the main target. A
common strategy for the enhancement of
the conductivity (σ) of polymers is the
addition of a conductive filler which can
form a network at a specific loading, named
percolation threshold (pc). When the filler
loading reaches the percolation threshold, the conductivity of the composite rises suddenly
and the conductivity-loading plot takes the characteristic S-shaped form, demonstrating the
three zones of conduction: insulating, percolating and conductive. In order for a composite to
conduct electricity, the fillers must form a network within the volume of the composite, so the
flow of electrons is not obstructed by the insulating areas of the matrix. Aggregated
structures that are interconnected with individual filler particles can also promote percolation,
along with the existence of a phase-separated, co-continuous morphology comprising of
graphene-rich and poor phases within the composite volume (volume-exclusion theory) 20, 21.
Therefore, reaching the percolation threshold in a composite depends on several
parameters: processing methods, state of dispersion, filer-matrix interactions, filler-filler
interactions, interphase, filler functionalization, crystallinity, defects and others. Graphene is
one of the most efficient fillers for the preparation of conductive composites due to its large
specific surface area, which leads to smaller percolation threshold 22, 23 and the existence of
the highly mobile electrons in graphene. The majority of the graphene field use classical
Figure 1. Electrical conductivity versus filler content for PET/graphene and PET/graphite composites. Solid lines are fits to the percolation theory. Inset:
log-log plot of volume electrical conductivity versus (φ-φc)
Graphene Core 1 D14.3 31 March 2017 7/ 22
percolation theory 24 to rationalize the conductive behaviour of composites:
𝜎" = 𝜎$ 𝜑&' − 𝜑"), where φgr is the volume fraction of graphene and φc is the percolation
volume fraction, while σc and σ0 are the conductivity of the composite and the intrinsic
conductivity of the filler respectively. t is the critical power law exponent and depends on the
system dimensionality, taking values of ~1.33 for 2D systems 25 and ~2 for 3D systems 26.
One example of the application of this theory is Zhang et al. who prepared PET/graphene
composites by melt compounding. They observed a pc of only 0.47 vol% graphene, while an
ultimate conductivity of 2.1 S/m was achieved with only 3 vol% graphene. The use of the
percolation theory was in good agreement with the experimental results (Fig. 1).
1.2. Conduction Mechanisms in Single Sheets
When there is disorder in an insulator-conductor composite, charge will percolate via a
hopping conduction mechanism 27. This involves the activation of charge carriers into free,
delocalized states 28. Electrons then hop between the available states to transport charge.
Hopping conduction mechanisms are split into two main mechanisms: nearest neighbour
hopping and variable range hopping. Both mechanisms normally proceed simultaneously,
but only one is usually the dominant mechanism. The general equation for hopping
conduction is 29: 𝜎 𝑇 = 𝜎$𝑒- ./
.
0
, where T is temperature, s0 and T0 are constants (although
they do have some a much weaker T dependence, it is much weaker effect) gamma is
hopping exponent. The hopping exponent depends on the dominant conduction mechanism,
which itself depends on the temperature of the system. At low temperatures, variable range
hopping is dominant. The hopping exponent then depends on the available dimensions of the
hopping as 𝛾 = 1𝐷 + 1 where D is the dimensionality. Mott law corresponds to 3D case, in
which p=1/4 30.
1.3. Conduction Mechanisms in 2D multilayered systems
In general, although various detailed studies on charge transport properties have been
published for single RGO sheets 31-34 clearly showing the Variable Rang Hopping (VRH)
regimes, a systematic study on more complex, multi-sheet systems is still lacking. To this
aim, CNR performed a systematic study of charge-transport mechanisms measuring
resistivity vs temperature curves (i.e. 𝜌 𝑇 ) of the macroscopic films of RGO. In such 3D
materials transport is highly anisotropic, taking place mostly intra-sheet (i.e. along single
RGO sheets, which are all oriented along the plane of the film), with however a significant
role of inter-sheet charge hopping (see Fig. 2).
Graphene Core 1 D14.3 31 March 2017 8/ 22
Figure 2. a) Resistivity vs temperature and b) corresponding activation energy W(T) measured on RGO films of thickness: (square) 2.4 nm, (circle) 3.1 nm, (triangle) 4.5 nm, (rhomb) 7.1nm, (star) 14.1 nm. Orange dotted line indicates the Tt temperature separating the two charge transport regimes. c) Scheme of the charge transport on (a) single RGO sheet and (b) thin film. The single sheet is represented as a long line of sp2, red points the inter-domain border composed of voids, C-O functionalities or other defects; the green arrow is the metallic like transport (no hopping) and the red arrow next to the border defects is the ES-VRH hopping. The extension of the localization length is approximately reported as crystal domains in RGO sheets and several crystal domains for thin films.
Unambiguous selection between hopping conduction mechanisms is a challenge due to an
intrinsic problem related to the fitting procedure. The Levenberg-Marquardt algorithm
typically used cannot be considered a robust approach for reproducing exponential or power-
law curves 35. The ambiguities can be avoided by exploiting the logarithmic derivative and
defining the activation energy as follow: 𝑊 = −𝜕𝑙𝑛𝜌 𝜕𝑙𝑛𝑇 36. Using this approach, the fitting
procedure results to be more “robust” and the VRH regime can be determined in a self-
consistent way: 𝜌 𝑇 = 𝜌$ ∙ 𝑒𝑥𝑝=/=
> Þ 𝑙𝑛𝑊 𝑇 = 𝐴 − 𝑝𝑙𝑛𝑇, where A is constant, p = 1/3,
1/4, 1/2 in the case of 2D-, 3D-Mott or Efros-Shklovskii VRH regimes. The W(T) curves
corresponding to the𝜌 𝑇 measurements are reported in fig. 2b clearly indicate the presence
of two regimes at different temperatures. At T lower than a transition temperature Tt the
linear behavior of W(T) clearly indicates the transport regime described by the regime ES-VRH for all the thicknesses (p = 0.5). The localization length (ξ), i.e. the spatial localization of
the charge involved in the hopping process, increases with the film thickness passing from
60±10 nm to 2.5±0.2 µm which results larger than one order of magnitude with respect to the
single RGO sheet. For higher T (T>Tt), the achieved plateau regime of W(T) corresponds to
a power-law dependence of𝜌 𝑇 due to the increasingly metallic properties of the system,
caused by an insulator to-metal transition.
3. Influence of Graphene Morphology on Composite Properties
1.4. Model graphene composites
An ideal graphene-based composite system would include continuous graphene sheets with
large lateral size, which would allow efficient load transfer from the matrix, perfect dispersion
Graphene Core 1 D14.3 31 March 2017 9/ 22
of the filler in the matrix and controllable electrical and thermal conductivities. The CVD
method offers the opportunity to make an experimental model of such an “ideal” system as it
produces high-quality graphene with large lateral dimensions. Vlassiouk et al. 37 prepared flat
laminates and scrolls of laminates by using a layer-by-layer approach between poly(methyl
methacrylate) (PMMA) and CVD graphene. The graphene loading in the flat laminate
composite was only 0.13 vol%, however the conductivity was amongst the highest reported
for graphene-based nanocomposites, at 810 S/m. This is a result of the ideal composite
architecture which allows enhanced electrical conduction and perfect orientation of the
graphene layers, without attributing heavy crumbling or even rolling of the graphene.
Moreover, CVD graphene does not require any reduction processes compared to the
majority of graphene flakes used in composites, which leads to high conductivity values.
Strano and co-workers subsequently prepared similar polycarbonate/CVD graphene layered
composites with a conductivity of S= 420 S/m at a filler content of 0.19 vol%, and a
percolation threshold as low as 0.003 vol% 38.
1.5. Graphene nanoplatelets
Graphene nanoplatelets (GNPs) are among the most popular materials used for reinforcing
polymer matrices because of their inherent tensile strength, and electrical and thermal
conductivity. However, the introduction of GNPs to improve electrical properties is not
straightforward, as several factors in material selection and preparation procedure govern the
resulting properties. Preparation method is particularly important in the case of GNPs as they
are prone to crumple, wrinkle and roll during composite processing. This is particularly
important when using GNPs in high-shear processes such as melt mixing. In contrast,
solution blending can help preserve the ideal form of the GNPs. Pang et al. 39 used a solvent-
assisted dispersion method followed by hot compression during the production of
UHMWPE/GNP composites and they achieved a percolation threshold at only 0.07 vol% filler
content. Another preparation method is in situ polymerization. This is known to produce
composites with a higher degree of dispersion; however it should be kept in mind that post-
processing methods such as hot pressing or injection moulding can also affect the dispersion
of the fillers and the ultimate conductivity of the composite. The different effect of solution
blending, in situ polymerization, and melt compounding on the conductivity of
polyurethane/graphene nanocomposites was investigated by Macosko and coworkers 40.
They found that the highest conductivity values were obtained from composites prepared via
solution blending. Melt mixing lead to particle reaggregation and particle attrition, which
reduced the lateral size of the graphene. For in situ polymerization, covalent bonds formed
between the matrix and the filler, which hindered direct contact between the fillers and
reduced the effective aspect ratio. Similar results were recently reported in the work of Xu et
Graphene Core 1 D14.3 31 March 2017 10/ 22
al. 41. Apart from the formation of a conductive filler network, the volume-exclusion principle
may also govern the conductivity of GNP-based composites. In this case, graphene is
selectively localized in specific areas in the volume of the composite, reducing the conductive
pathway and the respective percolation threshold.
Figure 3. Electrical conductivity for PS and nanocomposites, TEM image of PS/PLA (60:40) composite with 0.46 vol% graphene. The selective localization of graphene can be seen 42.
Koraktar and coworkers prepared conductive graphene/polystyrene and
MWCNT/polystyrene composites by solution mixing and reached percolation at a graphene
content of 0.33 vol% 42. The ultimate conductivity values of the graphene composites were
also 2-4 orders of magnitude higher than the MWCNT composites. When poly(lactic acid)
was incorporated in the graphene/PS composite, graphene was selectively localized in the
PS-rich regions, formed favourable π-π interactions and resulted in a network structure at
lower graphene contents, reducing the threshold 4.5 times, from 0.33 to 0.075 vol% (Fig. 3).
Moreover, functionalization of the filler can help towards the improvement of solubility and
processability, enhance the interactions between the filler and the matrix, and enable a
homogeneous dispersion. On the other hand, the covalent interactions between the fillers
and the matrix can sometimes disrupt the sp2 hybridized C atom conductive pathways and
reduce the electrical conductivity as in the work of Arzac et al. 43, 44. The composite
conductivity is also dependent on the contact type between the GNP flakes; plane to plane
contact is most effective rather than edge to edge or edge to plane, as a result of high
electron mobility and higher contact area between the different flakes. Therefore, forcing an
orientation on the filler during the preparation procedure can enhance the conductivity of the
composite. The correlations between all these parameters are quite difficult to establish. The
results of different preparation methods and graphene types in recent studies is summarised
in table 1 (Appendix) in an attempt to understand these correlations. The majority of the
works listed in the table are post-2010 as other reviews cover the literature up to 2011 45, 46.
Graphene Core 1 D14.3 31 March 2017 11/ 22
1.6. Thermally Reduced Graphene Oxide (TrGO) Composites
Thermally reduced graphene oxide flakes (TrGO) with specific surface areas of 600 to 950
m2/g have been prepared by oxidation of graphite followed by thermal expansion at
temperatures between 600 and 1000 °C 47. These thermal post-treatments increased the
carbon content of the GO materials up to 97 wt.% and lowered their resistivity to values from
1600 to 50 Ω×cm (depending on the reduction temperature), which are comparable to those
of compressed carbon black (CB) and natural graphite 47. The electrical conductivity of both
TrGO and the respective TrGO nanocomposites increases with increasing carbon content.
The presence of the remaining functional groups still promotes dispersion and interfacial
adhesion in many polymer matrices and that is the reason why TrGO is very promising to be
melt compounded in polymers of greatly different polarity. Several research groups have
employed TrGO materials to prepare thermoplastic nanocomposites based upon
polyethylene 48, maleic-anhydride grafted poly(propylene) 49, polystyrene 50 and
ethylene/methyl acrylate/acrylic acid copolymers 51. In comparison to conventional GO, TrGO
with its much higher degree of exfoliation, high specific surface area and higher carbon
content gave improved electrical properties at lower graphene content. Mulhaupt’s group
melt-compounded isotactic poly(propylene) (iPP), poly(styrene-co-acrylonitrile) (SAN),
polyamide 6 (PA6), and polycarbonate (PC) in a twin-screw mini-extruder together with TrGO 47. They showed that after melt extrusion the TrGO is uniformly dispersed and maintains
aspect ratios > 200. When loading TrGO into SAN, percolation was observed at 4 wt.%,
yielding a resistivity of 2.7×109 Ω×cm. By adding 12 wt.% of TrGO an ultimate specific
resistivity of 820 Ω·cm was obtained. For TrGO in PC-based nanocomposites, the authors
obtained a resistivity of 1.3×107 Ω·cm at 2.5 wt.% content, where the percolation threshold
was observed. By comparison, the conductivity of carbon-black filled composites was
considerably lower at the same filler contents. The incorporation of GO materials into
elastomers has also been reported. For example, natural rubber (NR) latex nanocomposites
have been reinforced with TrGO materials, showing an electrical percolation threshold at 3
phr of TrGO with values around 10-4 S/m 52. In addition, a comparative study on
carbon/styrene butadiene rubber (SBR) 53,54 has recently shown that TrGO exhibits superior
electrical performance with respect to other carbon nanofillers (including carbon black and
carbon nanotubes). This is in accordance with reports by other groups on enhanced
electrical conductivity on SBR/TrGO composites 54 and natural rubber composites found by
Ruoff and coworkers 55,56. In all the cases, TrGO has shown a very efficient formation of
percolation network. Compared to MWNTs, TrGO composites showed lower percolation
thresholds, which is attributed to the higher aspect ratio of TrGO 47,57. The low percolation
threshold of these graphene-based materials is of particular interest when aiming to improve
Graphene Core 1 D14.3 31 March 2017 12/ 22
the electrical conductivity of polymer nanocomposites at very low carbon content. The
maximum conductivity achieved with TrGO materials is however slightly lower (by about an
order of magnitude), compared to the equivalent MWCNT-based composites, probably due
to the presence of residual oxygen in TrGO. Random alignment of the flakes during melt
extrusion and presence of considerable amounts of defects could also play a role.
Some works report chemical compatibilisation strategies to achieve improved interfacial
adhesion between the TrGO and the polymer, as better adhesion leads to better dispersions.
An example is the work reported by Shim et al., where they coagulated SBR together with
raw, carboxylated and cetyltrimethylammonium bromide stabilized TrGO, and reported
improvements on the electrical conductivity showing percolation thresholds as low as 0.5
wt.% 54,58. Another example is the addition of TrGO to maleated linear low-density
polyethylene LLDPE and to its derivatives with pyridine aromatic groups by melt
compounding 57. In this report, very low electrical percolation thresholds (between 0.5 and
0.9 vol.%) depending on the matrix viscosity and the type of functional groups were found for
LLDPE/TrGO composites 57. However, due to the low density and very high surface area of
TrGO, the simple melt mixing procedure for the preparation of nanocomposites is challenging
and requires special handling and safety procedures. As a result, the alternative approach of
chemical reduction of GO materials is often selected, as described below.
1.7. Chemically Reduced Graphene Oxide Composites
Stable graphene dispersions are produced by chemical reduction of aqueous GO dispersions
using chemical reducing agents like hydrazine, sodium borohydride, hydroquinone, hydrogen
plasma, various alcohols, sulfur-containing compounds, or even vitamin C 59,60. These
treatments yield materials with less oxygen containing functionalities, more restored sp2
network, and higher electrical conductivity. The oxygen content of CRGO materials is similar
to that of TrGO produced at 400 ºC (~15% oxygen). Agglomeration during chemical
reduction can be prevented either by using very low concentrations or by adding surfactants
or polymers, during the reduction step 61-66. Approaches in which aqueous CRGO dispersions
were blended together with polymer latex to produce graphene containing composites with
good mechanical and electrical properties (~15 S/m at 1.6-2 wt.%) and very low percolation
thresholds (~0.8-0.9 wt.%) have been reported 66, 67. Ruoff and coworkers reported enhanced
electrical properties for both natural rubber (NR)/TrGO and NR/CrGO composites55, 56. They
found similar electrical performances for CrGO and TrGO materials, which were superior in
respect to CB. TrGO and CRGO nanofillers were also incorporated into styrene-butadiene
rubber (SBR) 53. When processed under identical conditions, CNT, multilayer graphene
(MLG) and TRGO show similar electrical conductivities and percolation thresholds, which
were all superior to other carbon fillers. In general, the ranking of carbon filler performance
Graphene Core 1 D14.3 31 March 2017 13/ 22
parallels their ability to form a percolating network. Furthermore, because TrGO is more
effectively exfoliated into single sheets, it often yields better electrical conductivity in
composites than other carbon nanofillers.
4. Comparison with other carbonaceous particles Avanzare has conducted extensive trials with a range of different GRMs and processing
conditions to obtain the highest possible conductivity at the lowest possible pc. They have
also benchmarked their GRMs against
other fillers, including multi-walled
nanotubes MWNTs (Figure 4). TrGO with a
very low content of oxygen (<1.5%at) and
large lateral size (40 μm) was found to
have a low pc in an epoxy matrix with a
high electrical conductivity at moderate
concentrations (0.5%v). It outperformed
both MWCNTs and relatively thin GNPs (6
nm thickness. By comparison, the
industrial-standard conductive filler, carbon
black, has a pc >10 wt%.
5. Effect of strain on percolated networks For some applications, composites are required to be flexible as well as conducting, e.g.
piezoelectric sensors and smart textiles. Graphene-based polymer composites have shown
excellent promise as strain sensors, functioning up to strains of 800% and monitoring signals
at 160 Hz 17. Combining graphene in a similar way with highly viscoelastic silicone polymer
(commonly found as Silly Putty) yielded a composite material with variable conductivity as
described by classic percolation theory (Fig. 5A) 68. More interestingly, the resistance varied
with strain in a controllable way with extremely high sensitivities of up to 500 (Fig. 5 B-C).
This level of dynamic sensing allowed them to monitor breathing and pulse, as well as the
movement of a spider (Fig. 5D). The mechanism for the change in resistance is still being
developed but is thought to be a combination of two processes, both of which lie in the
structure of the conducting network. The first is that as the composite stretches the number
of conductive pathways is reduced as graphene flakes become separated 69. A second
mechanism involves disconnected but closely spaced graphene sheets which the charge
carriers tunnel across; as these sheets become more separated, the tunnelling diminishes 69.
Both of these processes are reversible and hence the graphene-polymer composites are
able to perform many strain cycles (400 cycles with 60% strain 70) before failure. As well as
Figure 4. Electrical conductivity for chemically reduced and thermally expanded RGOx (1.4% at of Oxygen); GNP and MWCNT epoxy nanocomposites.
Graphene Core 1 D14.3 31 March 2017 14/ 22
strain sensors, graphene loaded composites could also be used for wearable heaters. These
are popular for the treatment of pain disorders and muscle strain. In contrast to strain
sensors, in this application a consistent resistance upon deformation is required. Without
this, localized heating could cause burns. Recent reports have shown that an addition of rGO
to a WPU/PEDOT:PSS composite did not alter the electrical conductivity of the network, but
did improve the thermal conductivity, yielding better thermal management 71.
0 2 4
0
2
4
6
8
10D
R/R
0
Strain, e (%)
7.9 vol%
G=350
B5 10 15
0
200
400
600
Sens
itivi
ty, G
f (%)
C
5 10 1510-11
10-9
10-7
10-5
10-3
10-1
s (S
/m)
f (%)
A
0 10 20 30 40-10
-5
0
5
10fc,e=1.75 vol%ne=11.9
DR
/R0 (
%)
t (s)
D
Figure 5: A) Conductivity as a function of volume fraction for polysilicone/graphene composites with the solid line representing percolation theory. B) Resistance change as a function of strain for a 7.9 vol% composite. C) In B), the slope represents the sensor sensitivity which is plotted versus graphene volume fraction. D) The polysilicone/graphene composite employed as an impact sensor, monitoring the footsteps of a small spider.
Conclusions The intrinsic conduction of GRMs depends on their thickness, grain structure, and degree of
defects/functionality. The majority of GRMs display conductivities that make them perfect
candidates for use as conductive reinforcements in polymer composites. The conductivity-
loading relationship is found to be described by classic percolation threshold, meaning that
the conductivity of a bulk composite is sensitive to flake morphology and processing history
of the composite. The values of the conductivities are sufficiently high for applications and
out-perform nanotubes processed under similar conditions. Finally, the percolated networks
are shown to be piezoelectric, providing a route to strain sensors capable of detecting a
spider’s footsteps.
Graphene Core 1 D14.3 31 March 2017 15/ 22
Appendix - References Table 1: Summary of electrical properties of graphene-based composites
Matrix Filler Preparation Method
Percolation Threshold
Ultimate DC Conductivity
(S.m-1)
Reference
PS GNP Solution blending 0.1 vol% 13.8 72 PS GNP Solution blending 0.33 vol% 3.5 42
PS GNP Electrostatic self-assembly 0.09 vol% 25.2 73
PS GNP Electrostatic assembly 0.054 vol% 46.3 74
PS CRGO Solution mixing + freeze-drying < 1 wt.% 15 67
sPS GNP Solution blending 0.46 vol% 4.7 75 PS/PLA GNP Solution blending 0.075 vol% 3 42 PMMA f-TRG Self-assembly 0.06 vol% 1.2 76 PMMA f-GNP Solution blending 0.8 vol% 20 77
PC TrGO
CB MWNT
Melt mixing 2.5 wt.% 2.5 wt.% 2.5 wt.%
0.001 0.1
0.006
47
PVC GNP Solution blending 0.1 vol% 5.8 78 PE f-GNP Melt mixing 0.83 vol% 0.01 79
UHMWPE
rGO Solution blending and hydrazinereduction
0.028 vol% 5 80
LLDPE TrGO Melt compounding 0.5-0.9 vol.% 10-4 57
PP
TrGO MLG CB
CNT EG
Melt compounding
< 5 wt.% 5 wt.%
7.5 wt.% 7.5 wt.%
--
1 x 10-2 3 x 10-3 3 x 10-5 4 x 10-6
--
81
iPP TrGO
CB MWNT Melt mixing
5 wt.% 5 wt.% 5 wt.%
0.02 3.3
3.1
47
PA6 TrGO
CB MWNT
7.5 wt.% 7.5 wt.%
--
7.1 x 10-3 2.2 x 10-8
-- 47
PA12 TrGO
N-TrGO Melt compounding 1-2.5 wt.%
1 wt.% 5.2 x 10-10
10-8 82
PA12
TrGO MLG350
EG CNTs
CB
Melt compounding
2.5 wt.%
2.5 wt.% 10 wt.% 5 wt.% 5 wt.%
8.9 x 10-6
1.2 x 10-6 6.6 x 10-12 1.6 x 10-5 1.3 x 10-5
83
Epoxy GNP Solution blending 0.52 vol% 0.05 84 Epoxy f-GNP Solution blending 0.16 vol% 10 85
EP TrGO Solvent free mixing method
1 wt.% 1 wt.%
2.0 x 10-10 1.0 x 10-9
86
Graphene Core 1 D14.3 31 March 2017 16/ 22
N-TrGO DMG
5 wt.% 8 x 10-9
PU rGO Solution blending 0.078 vol% 0.001 87
PU f-TrGO
CB CNT
In-situ polymerization 0.5-2 wt.%
2 wt.% 2 wt.%
1.4 x 10-11 1.3 x 10-11 1.9 x 10-11
88
TPU/PP f-rGO Solution-flocculation and
melt mixing 0.054 vol% ~ 10-6 89
NR GNP Latex self-assembly 0.62 vol% 0.03 90 NR rGO Solution blending 0.21 vol% 0.23 91 NR TrGO Latex technology 3 phr 10-8 52 NR CRGO Coagulation method 3 wt.% 10-4 55 NR TEGO Two-roll mill 0.02 vol.% 3.41 x 10-9 56
SBR Surface modified
MLGs
Hetero-coagulation method 0.5 wt.% 8.24 x 10-6 92
SBR f-3D-GO Latex coagulation 0.39 vol% ~ 10-2 93
SAN TrGO
CB MWNT
Melt compounding 4 wt.% 4 wt.%
12 wt.%
0.1 9
7 x 10-4
47
Graphene Core 1 D14.3 31 March 2017 17/ 22
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